Method and apparatus for fabricating radiation-redistributive devices

ABSTRACT

A method and apparatus for fabricating radiation-redistributive devices of the type comprising precisely contoured optical microelements each being adapted to redistribute incident radiation throughout a well-defined solid angle with uniform radiance throughout. The cutting stylus of a sound recording head is used as a cutting tool to contour such optical microelements in the surface of a workpiece. Desired contours are produced by shaping the cutting stylus to an appropriate cutting profile and by modulating the movement of the stylus in a vertical plane by applying an electrical signal of appropriate amplitude and waveform to the input of the recording head.

United States Patent [191 Wolfe et al.

[ METHOD AND APPARATUS FOR FABRICATING RADIATION-REDISTRIBUTIVE DEVICES [73] Assignee: Eastman Kodak Company,

Rochester, NY.

[22] Filed: Dec. 13, 1971 [21] Appl. No.: 207,334

OTHER PUBLICATIONS Publication: Journal of the Audio Engineering Society,

July 1964, Vol. 12, No. 3, Article Entitled The Westrex 3D Stereo Disk System, By C. S. Nelson and J. W. Stafford, pp. 178 and 179.

Primary Examiner-Francis S. l-lusar Attorney-Robert W. Hampton et al.

[57] ABSTRACT A method and apparatus for fabricating radiationredistributive devices of the type comprising precisely contoured optical microelements each being adapted to redistribute incident radiation throughout a welldefined solid angle with uniform radiance throughout. The cutting stylus of a sound recording head is used as a cutting tool to contour such optical microelements in the surface of a workpiece. Desired contours are produced by shaping the cutting stylus to an appropriate cutting profile and by modulating the movement of the stylus in a vertical plane by applying an electrical signal of appropriate amplitude and waveform to the input of the recording head.

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ROBERT /V. WOLFE BEVERLYE PALMER HARVEY 0. HOADLE) ROGER \S. VAN HEY/Vl/VG'EN INVENTORfi ATTORNEY F/Gl l8 METHOD AND APPARATUS FOR FABRICATING RADIATION-REDISTRIBUTIVE DEVICES CROSS-REFERENCE TO RELATED APPLICATIONS Reference is made to the commonly assigned U. S. Pat. application Ser. No. 207,082, entitled Radiation- Redistributive Devices, filed concurrently herewith in the names of James J. DePalma and Harold F. Langworthy.

BACKGROUND OF THE INVENTION The present invention relates to radiationredistributive devices, such as front and rear projection screens, illumination aids for photographs, advertisements, etc., and particularly to improvements in apparatus in methods for fabricating such devices.

In the above-referenced application, highly efficient radiation-redistributive devices are disclosed which, when irradiated by a source having a fixed position relative to the device, have the unique capability of redistributing such incident radiation only throughout a predefined field with the radiance of every point on the redistributing surfaces being substantially constant everywhere within such field radiance. The radiationredistributing surface of such devices is comprised of a multitude of contiguous optical microelements, each preferably being of a size such as to be unresolvable by the closest intended viewer, and contoured in accordance with a precise mathematical expression. The elements are arranged in contiguous rows which are defined by a series of parallel grooves of predetermined transverse cross section. Depth of the grooves undulates in a prescribed manner to define an optical microelement every half wavelength. Radiationredistributive devices of similar construction, but of lesser radiation-redistributing efficiency, are disclosed in U. S. Pat. Nos. 1,970,358, filed in the names of R. A. Bullet al.; 2,480,031, filed in the name of E. W. Kellogg; 2,758,200, filed in the name of K. Franck; and 2,984,152, filed in the name of A. I. Mihalakis.

Heretofore, a significant deterrant in the commercial development of radiation-redistributive devices of the above type has been the inability to shape numerous contiguous fine contours to the necessary precision by an economical process. See, for instance, the complexity of the manufacturing processes disclosed in the aforementioned patents.

SUMMARY OF THE INVENTION It is, therefore, an object of the invention to provide a relatively simple and economical apparatus and method for cutting extremely precise threedimensional contours in a workpiece which may subsequently be used as either a radiation-redistributive device or a master from which such devices can be subsequently molded or otherwise be economically replicated.

Another object of the invention is to provide an apparatus and method for fabricating both front and rear projection screens which comprise a multitude of con- 7 tiguous optical microelements, which are arranged in parallel linear rows, each microelement being capable of distributing substantially all image flux in such a manner that uniform image luminance results throughout a predefined audience space, and of directing substantially all incident light emanating from extraneous sources aay from such audience space.

In accordance with the present invention, it has been found that radiation-redistributive devices or masters in which the redistributing surface comprises a plurality of contiguous parallel grooves, each having a depth which varies along the groove length, can be economically fabricated using various equipment and techniques conventionally employed in the soundrecording industry. By mounting a sound-recording head in the tool holder of a conventional milling machine and by applying an electrical signal of appropriate amplitude and waveform to the input thereof, it has been found that the cutting stylus of the recording head can be used to cut precision contours in the surface of a workpiece as the workpiece and the stylus are moved relative to one another in a series of equally spaced, parallel traverses. Circuitry is provided for modulating the cutting position of the recording head stylus so as to cut optical microelements of such shape that, when irradiated by a source occupying a predefined position relative to the redistributive surface, substantially uniform radiance is produced throughout a prescribed field.

Other objects of the invention and its various advantages will become apparent to those skilled in the art from the ensuing detailed description of preferred embodiments, reference being made to the accompanying drawings wherein like reference characters denote like parts and wherein:

BRIEF DESCRIPTION OF THE DRAWINGS FIGS. 1 and 2 are magnified plan views of fragmentary portions of radiation-redistributive devices of the type readily manufactured by the methods and apparatus of the present invention;

FIGS. 3 and 4 are longitudinal and transverse sectional views of the device depicted in FIG. 1, taken along the section lines 3-3 and 44, respectively;

FIGS. 5 and 6 are longitudinal and transverse sectional views of the device depicted in FIG. 2, taken along the section lines 5-5 and 6-6, respectively;

FIG. 7 is a side elevational view illustrating a portion of the cutting apparatus comprising a preferred embodiment of the invention;

FIG. 8 is a constructional front elevational view of a portion of a stereo sound recording head;

FIG. 9 is a side view of the recording stylus and the support therefor;

FIG. 10 is a front profile of the cutting stylus illustrating the shape of the cutting edge;

FIG. 11 is a perspective view of apparatus adapted to translate a workpiece relative to the cutting apparatus depicted in FIG.'7;

FIG. 12 illustrates the manner in which the waveform of the stylus driving signal differs from the stylus motion produced thereby;

FIG. 13 is an electrical schematic of circuitry adapted to drive a cutting stylus to produce radiationredistribute devices of the type depicted in FIG. 1;

FIG. 14 is a scanning electron micrograph of a radiation-redistributive device fabricated in accordance with the method and apparatus of the invention;

FIGS. 15 and 16 are electrical schematics of circuitry adapted to drive a cutting stylus in such a manner as to produce radiation-redistributive devices of the type depicted in FIG. 2;

FIG. 17 illustrates the output of the shaping circuit of FIGS. 15 and 16; and

FIG. 18 illustrates a typical waveform applied to the cutting stylus when the y-position of the cutting stylus is displaced from workpiece center.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Radiation-redistributive devices of the types readily manufactured by the apparatus and method disclosed herein are illustrated in FIGS. 1 and 2. Devices of these types are disclosed in the aforereferenced co-pending application. The device of FIG. 1 is comprised ofa plurality of contiguous grooves 10, the depth of which continuously varies along the groove length in a periodic symmetrical manner, as best illustrated in FIG. 3. As shown in FIG. 4, the transverse cross section of the grooves depends only upon the groove depth where taken; that is, when taken at equal depths, the transverse cross section is the same from groove to groove. As the depth of each groove varies along its length, in accordance with a predetermined periodic waveform, optical microelements 11 are defined every one-half wavelength of the waveform, such microelements alternately varying from concave to convex. Where adjacent grooves meet, cusp lines 12 are formed. The width W of each microelement is, of course, determined by the groove width or the distance between adjacent cusp lines 12. The length L of each microelement is measured between points d, representing the average groove depth or the points at which the sense of the groove profile changes from concave to convex, or vice versa. When the device is employed as a projection screen, the size of each microelement is preferably too small to be resolved by the closest intended view; e.g., l square inches.

As indicated in the above-referenced application, the transverse and longitudinal cross sections of a convex microelement which is contoured to redistribute normally incident radiation in such a manner as to produce uniform radiance throughout a volume, bounded by viewing angles A and B (measured from the normal to the microelement in the plane of the cross section) must be substantially defined by at least a segment of the curve where n is the refractive index of the microelement (n being 1 in the case where the microelement is reflective); u and w are the microelement coordinates, w being measured in a direction parallel to the path of incident radiation, and 14 being measured in the plane of the cross section, perpendicular to w; and w has a value within the following limits:

cos A S w E 1, when f(w;n) is positive and cos B S w 1, when flwm) is negative; Similarly, the transverse and longitudinal cross sections of a concave microelement must be substantially defined by at least a segment of the curve wherein w has a value within the following limits:

cos B, when g(w;n) is positive; and cos A, when g(w;n) is negative.

The optical microelements comprising the surface depicted in FIG. 1, being identically contoured and oriented, redistribute normally incident radiation throughout a common solid angle which is symmetrical about the respective optical axis of each microelement. In order to maximize the surface efficiency, it is necessary to provide means for converging the optical axes of the microelements such that the solid angle through which each microelement redistributes radiation ofjust large enough to encompass the volume which is intended to receive the redistributed radiation. Converging the optical axes can be accomplished, for instance, by appropriatelycurving the surface, preferably spherically or cylindrically, or by employing the surface in combination with a Fresnel-like lens which serves to control the angle at which radiation strikes each of the microelements. A method of fabricating such appropriately curved surfaces is described subsequently herein.

The radiation-redistributive device illustrated in FIG. 2 is one which combines the Fresnel lens or curved surface requirement of the FIG. 1 device into each of the optical microelements comprising the redistributive surface. As best shown in the cross-sectional views of FIGS. 5 and 6, the microelements on the periphery of the surface are tilted with respect to those at the center so as to redistribute radiation emanating from a distant source, such as a projector lens, toward a central point situated in the volume intended to receive the redistributed radiation.

As set forth in the above-referenced application, in order for a convex optical microelement, irradiated by radiation incident at an angle 0 (measured from the normal), to produce uniform radiance throughout a volume bounded in a plane by angles A and B (also measured from the normal), the cross section of such microelement, taken in said plane, must be defined by at least a segment of the curve described by Equation (1) above where cos (A 0) S w s l, whenf(w;n) is positive and the microelement refractive;

cos (B 0') s w 5 I, when f(w;n) is negative and the microelement refractive;

cos (B 0) s w s I, when f(w;n) is positive and the microelement reflective;

cos (A 6) 5 w 5 I, when flw;n) is negative and the microelement reflective; and where sin 6' sin' O/n.

Similarly, every concave microelement comprising the surface illustrated in FIG. 2 must have a cross section defined by at least a segment of the curve described by Equation (2) above, where l s w 5 cos (B 6'), when g(w,'n) is positive and the microelement is refractive;

l s w 5 cos (A 6'), when g(w;n) is negative and the microelement is refractive;

l s w 5 cos (A 0), when g(w;n) is positive and the microelement is reflective; and

l s w 5 cos (B 0), when g(w;n) is negative and the microelement is reflective Before proceeding further with a detailed description of the apparatus and method for fabricating radiationredistributive devices of the type illustrated in FIGS. 1 and 2, it should be understood that such devices are merely examples of those which may be produced in accordance with the invention. The invention is being described with particular reference to these devices due to their unique and desirable capability of-redistributing radiation with substantially constant radiance throughout a precisely controlled field.

To fabricate radiation-redistributive devices or masters of the type having. surface contours such as those illustrated in FIGS=1 and 2, it has been found that various equipment and techniques conventionally employed in the sound recording industry can be used directly or in a modified form. In FIG. 7,-aside elevation of the cutting apparatus comprising apreferred embodiment of the invention is shown in a cutting position relative to a workpiece 20 wherein the microelements are to be formed. While'the microelements could be cut directly in any readily workable material whichitself could be used asthe radiation-redistributive-device, the preferred method of manufacture comprises the fabrication of a master in some workable material, such as acetate or wax, from which anegative' matrix or press tool of correct contour can be subsequently made. The negative matrix can then beused to produce a multitude of radiation-redistribution devices by such well-known economicalduplicating processes as;pressing, stamping, or injection molding. Preferred methods of making such devices from a master are described subsequently herein. It should be understood, however, that the apparatus and method of fabricating masters, as herein described, also applies to making the devices directly since, as stated above, the master itself could be used as a radiation-redistributive device.

As shown in FIG. 7, the cutting apparatus comprises a conventional stereo sound-recording head 30which includes a cutting stylus S. While a monophonic soundrecording head could be used, a stereophonic headis preferred due to the high quality of auxiliary equipment available for conventional stereo heads. As in all sound-recording heads, the cutting position of the stylus is determined by the waveform of an electrical signal applied to the recording head, such as'through input cables 31. The recording head is mounted on a milling machine tool holder 32 by a cylindrical fitting 33. Means are provided for controlling the vertical position of fitting 33 in the tool holder 32 so as to provide a coarse, vertical adjustment of the recording head 30 above the workpiece or master wherein the microelements are to be cut. The workpiece may comprise, for instance, an aluminum plate 36 having an acetate coating 37, the thickness of which is sufficient to receive the contours of the microelements. Recording head 30 comprises a cutting assembly 40 having a horizontally extending support arm 41 which is slidably mounted on precision ways disposed in a saddle 42. By this arrangement, the horizontal position of cutting assembly 40 can be varied. Set screws 43a and 43b serve to lock arm 41 in a desired horizontal position. Saddle 42 is pivotally mounted about pin 44disposed on recording head 30 so that the cutting stylus S, which forms apart of cutting assembly 40, can be pivoted into'engagement with the workpiece. The rotational movementof acam 46 serves to raise and lower the stylus relative to the workpiece surface by contacting anarm 47 which is rigidly coupled with saddle 42. The cutting force applied to the stylus is controlled by screw 48 which serves to adjust the tension in spring 49. The precise depth of cut is controlled by adjustment screw 50' surface of the workpiece a short, horizontal distance away from the stylus.

A sound recording head-which has been found particularly well adapted for such a cutting operation is the Westrex Corporation, Model 3D StereoDisc. As illustrated in FIG. 8 wherein a simplified constructional diagram of the mechanism which controls stylus movementis shown, each recording channel of the stereo recording head contains a magnetic coiled form assembly 60, each of which contains a driving coil 62 located in separated pole pieces 64 and 65 which are attached to a single magnet 66.

The coil assemblies are attached to the stylus holder through links 68 which are stifflon'gitudinally, but flexiblelaterally. These links are braced in the center to prevent excessive lateral compliance. This structure resultsin a stiff, forward driving system with a high c'ompliance in the lateral direction.

The supporting member for the stylus is shown in FIG. 9. The use of a cantilever spring 70 permits the stylus topresent a uniform impedance to complexmotions'in any direction in the vertical plane.

The cutting tip 72 of stylus S'is preferably sapphire, but can be fabricated from any material capable of cutting contours in the acetate coating of the workpiece. The cutting profile of the stylus is designed to conform with the desired transverse cross section of the microelements. A cutting profile which is substantially defined by Equation (1) is illustrated in FIG. 10, such profile being a somewhat flattened, half sinusoid. To assist in cutting the workpiece with the requisite accuracy, the stylus is heated by heating coil 73 to a temperature such as to soften the acetate layer. The heating current of approximately 0.7 Amperes for the heating coil can be taken from a 6.3 volt transformer with a resistance in series with the coil.

In cutting masters with the apparatus described above, the workpiece is moved relative to the heated cutting stylus in a series of equally spaced, parallel traverses. At the same time, the cutting position of the stylus is electronically varied relative to the workpiece to produce the desired longitudinal cross section or depth profile. Apparatus for moving the workpiece relative to the stylus is depicted in FIG. 11. As shown, workpiece 20 is supported by a table which is preferably fabricated from a non-magnetic metal, such as aluminum, so as not to interfere with the magnetic cutting assembly 40. In the upper surface of table 80, a circular groove is provided. At the base of groove 85 is an opening (not shown) which communicates with a nozzle 86 located on the edge of the table. Attached to nozzle 86 via hose 87 is a vacuum source (not shown). By this arrangement, the workpiece is securely fastened to the surface of table 80 by a vacuum coupling. Table 80 is mechanically secured to a movable workbed 88 comprising the x-y table 89 of a milling machine. Workbed 88 is movable in the x direction and its position is controlled with precision by a conventional stepping motor 90 which acts through lead screw 91. Workbed 88 itself rides atop a movable carriage 93, also forming a part of the x-y table of the milling machines. Carriage 93 is movable in the y direction by a hydraulic-pneumatic motor 95 which precisely controls the rate at which carriage 93 moves via piston rod 96.

To move the cutting stylus in a vertical plane and at a rate which, when the workpiece is moved at a constant rate relative thereto, results in the longitudinal cross section or depth profile desired, the same signal must be applied to both drive coils 62. Moreover, since the stylus is not mounted for vertical movement, but rather for pivotal movement on the cantilever spring 70, so as to traverse an arcuate path as shown in phantom lines, it is necessary to drive the stylus with a somewhat different waveform than that which corresponds to the longitudinal cross section desired. Referring to FIG. 12, when a waveform 101 is applied to the cutting stylus, the resulting groove has a depth profile as shown in the asymmetrical waveform 102. To compensate for the asymmetry, it is necessary to drive the cutting stylus with a counterbalancing asymmetrical waveform 103 which the arcuate stylus movement converts to the depth profile desired (e.g., waveform 101). It is interesting to note that in the sound recording art, such asymmetry is automatically compensated for during playback by the pickup stylus which is also pivotally mounted and moves along an arcuate path similar to that along which the cutting stylus used to cut the original master moved. In manufacturing the radiationredistributive devices of the invention, however, such asymmetry must be compensated for by circuitry for modifying the desired waveform accordingly.

In FIG. 13, electronic circuitry is schematically illustrated for driving the cutting stylus in such a manner as to cut microelements having longitudinal cross sections substantially defined by the above equations. The waveform defined by the above equations differs from a true sinewave in that the peaks are flattened, relative to the lower-amplitude portions of the wave. As mentioned hereinabove, to produce a groove depth modulation in accordance with a desired waveform, it is necessary to drive the cutting stylus with an asymmetrical waveform which is converted to the desired waveform by the arcuate stylus movement. To produce a waveform which when applied to the cutting stylus produces a groove depth profile substantially defined by Equations (1) and (2), the output (sin 2:) of a conventional sinewave generator 109 is first asymmetrically distorted by asymmetrical circuit 110 to compensate for the arcuate stylus movement, and then shaped by shaping circuit 111 to produce the waveform required for appropriately driving the cutting stylus S. It has been found that by adding to the sine waveform a small amount of its second harmonic, the requisite distortion can be substantially achieved. A squaring circuit 112, such as an analog multiplier module, is used to generate the second harmonic waveform (sine 2x) from the fundamental. Capacitor Cl is used to eliminate the dc component of the second harmonic signal so as to produce a positive and negative-going signal. Since the midpoint of the sin 2x waveform lags the sin 1: waveform by 45, it is necessary to fed the output of the sine wave generator through a simple RC phase lagging circuit 113. In this manner, the two waves are added while in phase by operational amplifier Al. The amount of asymmetry in the output of amplifier Al depends, of course, on the peak-to-peak amplitude of the added second harmonic. Potentiometer Pl serves to vary the second harmonic amplitude prior to being added to the fundamental.

To produce the desired waveform from the asymmetrically distorted sine wave output of circuit 110, such output is fed to the shaping circuit 111. This input signal is segmented by reason of having to overcome successively the forward voltage drop cross diodes D1-D10. Diodes Dl-DS and D6-D10 serve to segment the positive and negative-going portions of the input signal, respectively. Operational amplifier A2 serves to sum the contributions of the various segments to produce a difference signal Ax having a waveform representing the difference by which the desired waveform (Equation (2) plug distortion) differs from the asymmetrically distorted sine wave. The contributions of the individual segments to the output of amplifier A2 are adjusted by varying the values of resistors Rl-RS. The output of amplifier A2 is adjustable in amplitude by potentiometer P2. By simply adding the difference signal Ax, which is of a polarity reversing effect of amplifier A2, to the unshaped signal, the desired waveform for driving the cutting stylus is achieved. Such addition is performed by operational amplifier A3. Resistors R6 and R7 and potentiometer P3 serve to control the gain provided by the summing amplifier A3. The output of amplifier A3 is then applied to both driving coils of the stereo recording head (180 out of phase) to drive the cutting stylus.

To fabricate the screen depicted in FIG. 1, a start button is pressed which pivots the recording head about pin 44 into a cutting position, causes pneumatic motor 95 to move the carriage 93 in the y direction and causes the above-described electronic circuitry to drive the cutting stylus according to the waveform of the electrical signal applied thereto. After cutting a groove of predetermined length, a microswitch (not shown) is actuated by the carriage 93 which serves to stop pneumatic motor 95, activate a solenoid which moves cam 46 of the recording head clockwise into a position to pivot the cutting assembly into an onoperative position, and actuate stepping motor so as to move workbed 88 a predetermined distance in the x direction. The microswitch also returns carriage 93 to its starting position on the y-axis which, in turn, actuates a second microswitch. When actuated, the second microswitch rotates cam 46 counterclockwise to permit the recording head to pivot into an operable cutting position, and the cutting process is repeated. This process continues without interruption until the entire master has been cut.

As the heated stylus S cuts a groove in the workpiece, a continuous sliver or chip is extricated from the workpiece surface. To continuously draw this sliver away from the workpiece, a vacuum nozzle 121 (shown in FIG. 7) connected to a vacuum source through hose 122, is positioned adjacent stylus S during the cutting operation. The maximum depth of cut produced by the stylus in the workpiece is controlled by the advance ball 51 which rides on an uncut portion of the workpiece, near the stylus. The recording head includes a mechanism for maintaining the distance between the stylus tip and the base of the ball constant. Preferably, the groove spacing and minimum groove depth are set such that no land or fiat areas exist between adjacent grooves.

A scanning electron micrograph of a portion of a screen master fabricated with the apparatus and method set forth hereinabove is provided in FIG. 14. As is apparent, the spatial frequency of the grooves 10 is substantially less than that of the depth variations. The fact that the depth profiles are not prefectly in phase from groove to groove has been found to have no substantial effect on screen performance.

To fabricate radiation-redistributive devices having transverse and longitudinal cross sections such as depicted in FIGS. 5 and 6, respectively, it is necessary to drive the cutting stylus with a signal having a wave form which varies in accordance with the y -position of the stylus on the workpiece surface. Moreover, it is also necessary to vary the angle at which the stylus contacts the workpiece in accordance with the x-position of the stylus on the workpiece surface. Thus, only at the center (y x 0) do the microelements comprising the FIG. 2 device have the same cross sections as those which comprise the FIG. 1 device.

To maintain the proper orientation between the cutting stylus and the workpiece during movement of the workpiece in the x direction, the milling machine tool holder is motorized so as to be capable of tilting the recording head' in the x-z plane in accordance with an electrical input signal. The x-z position of the stylus is changed after each groove is cut so that at all times during the cutting operation, the angle t between the longitudinal axis of the stylus and the normal to the work surface must be t= tan (p/x) where x is measured from the center of the workpiece center, and p is the projection in the z plane of the di- ,tance from the workpiece centerto the location of the irradiating source. The motorized tool holder of the milling machine is controlled by the output of stepping motor 90.

Circuitry for driving the cutting stylus to produce a depth profile such as illustrated in FIG. 5 is illustrated in FIGS. and 16. To facilitate an understanding of the circuitry, only that portion which is used to cut half of the master, either the upper or lower half, is initially described. The additional logic circuits required to cut the entire surface are illustrated in FIG. 16. i

i In FIG. 15, circuitry is disclosed for generating the electrical waveform whereby the cutting stylus can be modulated to produce microelements having depth profiles similar tothose illustrated in FIGS. 60" and 6b. It has been found that the required electrical waveform can be achieved by adding a sawtooth waveform, in varying amounts depending upon the y-position of the cutting stylus, to the asymmetrical waveform required for producing'the desired depth profile at the y 0. To generate the necessary sawtooth waveform, a sawtooth generator 130 is provided, such generator comprising a flip-flop 131, a limit detector 132, diode D15, capacitor C5, resistors R12 and R13, and operational amplifier A7. Amplifier A7 is connected as an integrator to give a linear ramp while the voltage at q, V,,, is constant. When V is negative, the ramp output V of the sawtooth generator goes positive. WI-Ien V, reaches the positive threshold of limit detector 132, flip-flop 130 is switched to make V positive, at which time V, becomes negative-going. When V, reaches the negative threshold of limit detector 132, flip-flop 130 is again switched to make V, negative again. Operational amplifier A7 preferably has complementary outputs, and the limit detector 131 acts by detecting the negative limit of first one output and then the other. The slopes of the positiveand negative-going ramps of the sawtooth are controlled by diode D15 and resistors R12 and R13, the latter being variable. Diode D15 is nonconducting when V, is negative, and conducts when V, is positive. Therefore, the positive-going ramps is slower than the negative-going ramp because the slope of the-former is determined by the current flowing through resistor R12 only, whereas the slope of the latter is determined by the current flowing through both resistors R12 and R13. By varying the value of resistor R13, the slope of the negative-going ramp can be varied.

The sawtooth output of generator 130 is then fed through a non-linear shaping circuit 140 which, as shown in FIG. 17, acts to convert the positive-going linear ramp 141 to the asymmetrical waveform 142 required to drive the cutting stylus to achieve the desired shape of the microelements at the center of the master. To prevent that portion of the shaping circuit output which occurs during the flyback (fast-sloped negativegoing ramp) of the sawtooth from being applied to the cutting stylus, a blanking gate 143 is provided which transmits the input signal from the shaping circuit only when V is negative. The slope of ramp 141, as illustrated in FIG. 17, is sufficient only to produce a depth profile for the microelements at y 0. To produce the required depth profile as the y-position of the cutting stylus gradually increases, it isnecessary to gradually tilt the y 0 depth profile such that each microelement redirects image-light in the same direction in the y,z plane. Such gradual tilting is accomplished by gradually adding, as the y-position of the cutting stylus gradually increases, the sawtooth waveform to the output of the shaping circuit 140. Such addition is accomplished by operational amplifier A8. To vary the contribution of the sawtooth waveform, resistor R15 is mechanically varied in concert with the y-position of the carriage 93. In FIG. 18, the output of the above circuit is illustrated when the cutting stylus is at a position displaced from the screen center.

To provide an electrical waveform whereby the cutting stylus can be modulated in such a manner as to properly vary the groove depth on both sides of the master center, it is necessary to provide circuitry for interchanging the direction of the fast and slow slopes of the sawtooth (i.e., change the senseof the sawtooth) as the cutting stylus passes across the center line of the master. Moreover, it is necessary to switch the shapeblanking so that gate 143 operates during the fastsloped portion of the sawtooth, whether positive or negative-going. The required circuitry is illustrated in FIG. 16. To switch the sense of the sawtooth at y 0, the fast-slope diode D15 of FIG. 15 is replaced by an exclusive OR gate 150, the output of which is controlled by a switch 151 on the milling machine carriage, switching from one state to another as the screen center (y 0) passes the cutting stylus. To properly cut the master on both sides of y 0 an additional non-linear shaping circuit 152 and blanking gate 153 are required since the asymmetry caused by the arcuate movement of the cutting stylus does not depend on the particular portion of the master being cut. The output of the proper shaping circuit is supplied to amplifier A8, during the slow ramp portion of the output of the sawtooth generator, through blanking gates 143 and 153 which are controlled respectively by NAND gate 155 and OR gate 156.

After making a master in accordance with the afore described method and apparatus, radiationredistributive devices can be produced therefrom by making a negative matrix or master from the original, and casting positives in a resinous material, from the negative master. Preferably, the negative master is made from General Electric RTV-6O silicone rubber which is prepared by adding three grams of dibutyl tin dilaurate RTV curing catalyst to two pounds of the RTV-60 rubber, agitating the mixture with an electric stirrer for five minutes and then placing it in a bell jar which is then evacuated to a pressure of 150 microns of mercury for about twenty minutes. Upon fixing sidewalls to the edge of the original master, the RTV rubber mixture can then be poured into this mold so that no air is entrapped. After curing, the rubber mold, which is a negative master, can then be used to replicate positive radiation-redistributive devices.

To fabricate spherically or otherwise curved radiation-redistributive devices (e.g., front projection screens) from a planar master of the type depicted in FIGS. 1, 3 and 4, the rubber negative mold is disposed on an appropriately curved support prior to casting. A Maraglas epoxy resin, after being degassed, is then poured into the mold. After heating in an oven at 200 F for several hours to harden the resin, the casting is coated with an aluminum coating to form a reflective radiation-redistributive device. Refractive devices can be made from such masters by incorporating a Fresnellike lens on the rear surface of the casting replicated therefrom.

From the foregoing, it is apparent that an exceptionally simple apparatus and method have been provided for producing radiation-redistributive devices of relatively complex surface contours. Heretofore, such contours could not be as economically fabricated. According to the instant'invention, variations in surface contour, to alter, for instance, the angle through which incident radiation is redistributed can be achieved simply by varying the values of circuit elements which comprise the stylus driving circuitry. Once the stylus cutting profile and drive circuitry to achieve a desired microelement contour has been provided, masters can be fabricated in a matter of hours, as compared with several days or even weeks required by prior art techniques. Moreover, because of the responsiveness of the cutting stylus, the desired contours of microelements can be produced with extreme accuracy, thereby providing higher quality devices than were heretofore possible.

This invention has been described in detail with particular reference to preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention.

We claim:

1. A method for making a radiation-redistributive device having a surface defining a plurality of rectilinear grooves, each groove varying in depth along the groove length in accordance with a predetermined undulating waveform and having a transverse cross section defined by a predetermined arcuate curve, said method comprising the steps of:

moving a cutting stylus and a surface in which such grooves are to be formed relative to each other in a series of parallel traverses to cut sequentially a plurality of rectilinear grooves in such surface,

such stylus having a cutting profile in accordance with said predetermined arcuate curve, and such traverses being made in a direction parallel to that of the intended grooves, and

while cutting each groove, modulating the cutting depth of the stylus by applying an electrical signal thereto of such waveform that the position of said stylus is varied in a plane perpendicular to said surface whereby a groove having a depth profile in accordance with said predetermined undulating waveform is cut in said surface.

2. The method of claim 1 wherein said cut is made with the cutting stylus of a sound recording head.

3. Apparatus for making a radiation-redistributive surface which surface includes rectilinear grooves, each groove having a cross section in a first plane transverse to the groove which is curved to give a desired light distribution in said plane and has a depth profile which undulates according to a waveform to give a desired light distribution in a second plane perpendicular to said first plane and to said surface, said apparatus comprising:

a sound-recording head including a movably mounted cutting stylus having a cutting profile which is curved to correspond to said cross section, and control means operatively coupled to said stylus and responsive to the waveform of an electrical signal for varying the position of said stylus in accordance with the instantaneous amplitude of said waveform; A

means for moving said stylus and a surface in which such grooves are to be formed relative to each other in a series of parallel traverses to cut rectilinear grooves in said surface; and

circuit means coupled to said control means for generating an electrical signal having a waveform which, during relative movement between said stylus and said surface, causes the position of said stylus to vary in such a manner as to cut grooves having said depth profile.

4. The apparatus according to claim 3 wherein said circuit means comprises means for generating a sine wave; means operatively coupled to said sine wave generating means for producing an error signal representing the manner in which said depth profile differs from a sine wave; and means operatively coupled with said sine wave generator and said error signal producing means for combining said error signal with a sine wave to produce a signal having a waveform substantially identical to said groove depth profile.

5. The apparatus according to claim 2 wherein said circuit means further comprises means for generating a sawtooth waveform, and means operatively coupled to said moving means for adding said sawtooth waveform to said electrical signal in an amount dependent upon the distance between said stylus and a line perpendicular to said grooves and passing through the center of said surface, whereby the optical axes of the microelements in each row converge at a point spaced from said surface.

Inventor(s) UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent: No. 3,765,281

'Dated October 16. 197% Robert N. Wolfe, Beverly F. Palmer, Harvey O. Hoadley,

Column Column Column Column Column Column Roger S. VanHeyningen It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

. line lines 26 line Signed and sealed (SEAL) Attest:

EDWARD I'LFLETCHERJR. Attesting Officer "of" should read --is- "separated" should read --separate--;

"sine" should read --sin "onoperative" should read --inoperative-; "prefectly" should read -perfectly-q and 27, "ditance" should read -distance--.

this 9th day of April l97h.

C. MARSHALL DANN Commissioner of Patents 

1. A method for making a radiation-redistributive device having a surface defining a plurality of rectilinear grooves, each groove varying in depth along the groove length in accordance with a predetermined undulating waveform and having a transverse cross section defined by a predetermined arcuate curve, said method comprising the steps of: moving a cutting stylus and a surface in which such grooves are to be formed relative to each other in a series of parallel traverses to cut sequentially a plurality of rectilinear grooves in such surface, such stylus having a cutting profile in accordance with said predetermined arcuate curve, and such traverses being made in a direction parallel to that of the intended grooves, and while cutting each groove, modulating the cutting depth of the stylus by applying an electrical signal thereto of such waveform that the position of said stylus is varied in a plane perpendicular to said surface whereby a groove having a depth profile in accordance with said predetermined undulating waveform is cut in said surface.
 2. The method of claim 1 wherein said cut is made with the cutting stylus of a sound recording head.
 3. Apparatus for making a radiation-redistributive surface which surface includes rectilinear grooves, each groove having a cross section in a first plane transverse to the groove which is curved to give a desired light distribution in said plane and has a depth profile which undulates according to a waveform to give a desired light distribution in a second plane perpendicular to said first plane and to said surface, said apparatus comprising: a sound-recording head including a movably mounted cutting stylus having a cutting profile which is curved to correspond to said cross section, and control means operatively coupled to said stylus and responsive to the waveform of an electrical signal for varying the position of said stylus in accordance with the instantaneous amplitude of said waveform; means for moving said stylus and a surface in which such grooves are to be formed relative to each other in a series of parallel traverses to cut rectilinear grooves in said surface; and circuit means coupled to said control means for generating an electrical signal having a waveform which, during relative movement between said stylus and said surface, causes the position of said stylus to vary in such a manner as to cut grooves having said depth profile.
 4. The apparatus according to claim 3 wherein said circuit means comprises means for generating a sine wave; means operatively coupled to said sine wave generating means for producing an error signal representing the manner in which said depth profile differs from a sine wave; and means operatively coupled with said sine wave generator and said error signal producing means for combining said error signal with a sine wave to produce a signal having a waveform substantially identical to said groove depth profile.
 5. The apparatus according to claim 2 wherein said circuit means further comprises means for generating a sawtooth waveform, and means operatively coupled to said moving means for adding said sawtooth waveform to said electrical signal in an amount dependent upon the distance between said stylus and a line perpendicular to said grooves and passing through the center of said surface, whereby the optical axes of the microelements in each row converge at a point spaced from said surface. 